Need advice on where to print menus - Japanese Steakhouse

Hi, I am a graphic designer and have recently been commissioned to redesign a client's menu. They are a japanese steakhouse and cook the food in front of the customers and so the menus are exposed to heat from the stovetop. She said she is not satisfied with their current menus, which I think they just had printed locally and had some ordinary thick lamination put over them. The laminate has bubbles in it and looks generally cloudy.
Does any one have a recommended website they use for printing menus?
I understand that no menu is going to withstand being set on top of a griddle, but I just need something that is better quality than what they currently have, but won't cost an arm and a leg. Thanks!

you would probably be better served going to a local printer and seeing what they have.  You could probably even get some samples and see how they work.  Based on what you say you need, I probably would not buy online as if they do not work, you own them
 
al